Rota-Baxter coalgebras and Rota-Baxter bialgebras
Tianshui Ma, Linlin Liu
TL;DR
This paper introduces Rota-Baxter coalgebras and bialgebras, constructing them from Hopf module coalgebras and exploring their structures and examples, advancing the algebraic theory of Rota-Baxter operators.
Contribution
It provides a new construction method for Rota-Baxter coalgebras from Hopf module coalgebras and introduces Rota-Baxter bialgebras with illustrative examples.
Findings
Construction of Rota-Baxter coalgebras from Hopf module coalgebras
Derivation of pre-Lie coalgebra structures via Rota-Baxter coalgebras
Introduction and examples of Rota-Baxter bialgebras
Abstract
We give a construction of Rota-Baxter coalgebras from Hopf module coalgebras and also derive the structures of the pre-Lie coalgebras via Rota-Baxter coalgebras of different weight. Finally, the notion of Rota-Baxter bialgebra is introduced and some examples are provided.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms